Ncert Exercises & Solutions

8.14 A Saturn year is 29.5 times the earth year. How far is Saturn from the sun if the earth is 1.50 × 108 km away from the sun?

A s w e k n o w t h a t,

T^{2} \propto R^{3}

\Rightarrow {(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{R_{1}}{R_{2}})}^{3}

\Rightarrow R_{2} = R_{1} {(\frac{T_{2}}{T_{1}})}^{2 / 3}

= (1.5 \times 10^{8}) \times {(\frac{29.5}{1})}^{2 / 3}

= 1.5 \times 10^{8} \times 9.547 = 14.3 \times 10^{8} k m

= 1.43 \times 10^{12} m